Question
Elinor determined that a triangle with side lengths 6, 10, and 8 does not form a right triangle using the following steps:
62+102=82
36+100=64
136≠64
Is her answer correct?
(1 point)
Responses
No, she should've added 62
and 82
and compared that to 102
.
No, she should've added 6 squared and 8 squared and compared that to 10 squared.
No, she should've added 102
and 82
and compared that to 62
.
No, she should've added 10 squared and 8 squared and compared that to 6 squared.
No, she should've added 62
from 102
and compared that to 82
.
No, she should've added 6 squared from 10 squared and compared that to 8 squared.
Yes, she is correct.
62+102=82
36+100=64
136≠64
Is her answer correct?
(1 point)
Responses
No, she should've added 62
and 82
and compared that to 102
.
No, she should've added 6 squared and 8 squared and compared that to 10 squared.
No, she should've added 102
and 82
and compared that to 62
.
No, she should've added 10 squared and 8 squared and compared that to 6 squared.
No, she should've added 62
from 102
and compared that to 82
.
No, she should've added 6 squared from 10 squared and compared that to 8 squared.
Yes, she is correct.
Answers
GPT-4o mini
To determine if a triangle with side lengths 6, 10, and 8 is a right triangle, we can apply the Pythagorean theorem. The theorem states that for a right triangle with sides \( a \), \( b \), and hypotenuse \( c \), the relationship \( a^2 + b^2 = c^2 \) holds.
First, we need to identify which side is the longest to determine the hypotenuse. Here, the side lengths are:
- \( 6 \)
- \( 8 \)
- \( 10 \) (this is the longest side)
Next, let's calculate the squares of the lengths:
- \( 6^2 = 36 \)
- \( 8^2 = 64 \)
- \( 10^2 = 100 \)
Now we should check if the relationship \( 6^2 + 8^2 = 10^2 \) holds:
- \( 36 + 64 = 100 \)
- \( 100 = 100 \)
Since \( 6^2 + 8^2 = 10^2 \) holds true, the triangle with side lengths 6, 10, and 8 does form a right triangle.
Given this analysis, we can see that Elinor's determination that it does not form a right triangle is **incorrect**. Her calculations and comparison were not properly aligned with the Pythagorean theorem, as she didn't set up the equation correctly.
The correct response to the question would be:
**No, she should've added \( 6^2 \) and \( 8^2 \) and compared that to \( 10^2 \).**
First, we need to identify which side is the longest to determine the hypotenuse. Here, the side lengths are:
- \( 6 \)
- \( 8 \)
- \( 10 \) (this is the longest side)
Next, let's calculate the squares of the lengths:
- \( 6^2 = 36 \)
- \( 8^2 = 64 \)
- \( 10^2 = 100 \)
Now we should check if the relationship \( 6^2 + 8^2 = 10^2 \) holds:
- \( 36 + 64 = 100 \)
- \( 100 = 100 \)
Since \( 6^2 + 8^2 = 10^2 \) holds true, the triangle with side lengths 6, 10, and 8 does form a right triangle.
Given this analysis, we can see that Elinor's determination that it does not form a right triangle is **incorrect**. Her calculations and comparison were not properly aligned with the Pythagorean theorem, as she didn't set up the equation correctly.
The correct response to the question would be:
**No, she should've added \( 6^2 \) and \( 8^2 \) and compared that to \( 10^2 \).**